The police chief in charge of the raid on Sir Cliff Richard's home has apologised to the singer after MPs said he showed a "gross lack of competence" for doing a controversial "sweetheart deal" with the BBC.

David Crompton, the chief constable of South Yorkshire police, was roundly condemned by members of the House of Commons home affairs select committee on Tuesday after the BBC broadcast pictures of last month's search from a helicopter above Richard's £3.1m Berkshire apartment.

Crompton told MPs he did a deal with the corporation after its reporter, Dan Johnson, received a tip-off. Crompton said he feared if the force did not co-operate the BBC would run with the story and ruin his force's investigation.

MPs expressed disbelief that Crompton, who criticised the BBC's subsequent coverage as "intrusive", had not done more to try to prevent it from running the story.

The committee chairman, Labour MP Keith Vaz, said: "We have been amazed at the sheer incompetence of the way this has been dealt with.

"Criminals must be rubbing their hands with glee at the thought of dealing with your officers who appear to give in at the first opportunity. You blame everybody else but as far as you are concerned you did everything right."

Crompton said: "We had a job to do. I apologise to Sir Cliff if we were insensitive about the way we did that. We had an investigation, the problem for us was that investigation could never be done in a low profile way because it was fatally compromised from the outset."

The singer's apartment was searched by officers from South Yorkshire and Thames Valley police as part of an investigation into an alleged sexual assault on a boy at a religious event in 1985.

Richard, who was on holiday in Portugal at the time of the search, has firmly denied any wrongdoing.

BBC director general Tony Hall, who also gave evidence to MPs, defended the scale of the BBC's coverage of the raid on 14 August, including the use of a helicopter, after critics accused it of participating in a "witch-hunt" and behaving like the worst tabloid newspaper.

Hall said: "In a variety of different ways allegations of sexual abuse going back many, many years are sadly, regrettably a matter of public interest. What you saw from the air was a number of police cars and you saw the scale of the operation."

Asked if he felt any sympathy for the singer because of the extent of the BBC's coverage, Hall said: "Our job was to make sure what Sir Cliff had to say about the search and about his own innocence was properly reflected."

BBC executives were at odds with Crompton about the negotiations that led to the South Yorkshire force giving the corporation full details of the raid a day in advance, including pictures of the property.

Crompton said the BBC's reporter, Dan Johnson, approached his officers with all the facts in his possession. Hall said Johnson only had a name and South Yorkshire police had then "given us a story and made no attempt to stop us running the story".

The BBC's director of news and current affairs, James Harding, also denied Crompton's claim that Johnson had named the Metropolitan police, specifically its Operation Yewtree inquiry into sexual abuse allegations, as the source of his story. He said Johnson "did nothing to disclose his source".

Hall said if Crompton had approached him or any of his senior team asking him not to run a story he would have taken it "extremely seriously. Would we have engaged with the police? Absolutely."

But Crompton said he did not escalate the issue with the BBC management because he thought they would run the story anyway.

"We were placed in a very difficult position because of the original leak," he said. "My concern was if we showed the BBC the door, the very clear impression which had been left ... was that they were likely to publish the story that would have impeded the investigation.

He added: "I didn't have that much faith that we could trust it wouldn't be published. You only have to look at Leveson to find a number of examples that were core to that particular inquiry where the media decided to publish anyway. That was something very much in my mind."

Vaz said the way Crompton had described it "sounds like blackmail". Crompton replied: "Blackmail is a very strong word. It put us in a very difficult position."

Crompton, who admitted he had been "a little naive", said he was "confident that we made the right decision in difficult and unusual circumstances". He described the BBC's coverage as "disproportionate" and "made our actions look heavy handed and intrusive. I do regret that. Frankly it didn't make any of us look good".

The committee is to publish texts and emails relating to the affair, from both the BBC and South Yorkshire police, on Wednesday. It has also written to Richard and said it would publish his response.

Vaz told Crompton he had been "more than a little naive". He said the BBC had acted "perfectly proportionately" in its reporting of the affair. Further questions will be put to Crompton when he returns in front of the committee next week.